## The Journal of Symbolic Logic, Volumes 7-8Alonzo Church, Cooper Harold Langford Association for Symbolic Logic., 1942 - Logic, Symbolic and mathematical Publishes original scholarly work covering the entire field of symbolic logic, reflecting its role in philosophy and in mathematics. Includes newer aspects of logic, related to other disciplines such as computer science and linguistics. |

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### Contents

The BuraliForti paradox By Barkley Rosser | 1 |

New sets of postulates for combinatory logics By Barkley Rosser | 18 |

A formal theorem in Churchs theory of types By M H A Newman | 28 |

12 other sections not shown

### Common terms and phrases

abbreviation adapted to F Alonzo Church application arbitrary assigned Association for Symbolic axiom of choice axiom of infinity axiomatic Barkley Rosser Boolean algebra brackets Burali-Forti Paradox calculus cardinal number class of pairs class theorem combinatory complete concept condition consequence contains converse domain decision problem deductive defined definition denote element enumerable sequence equivalent Ernest Nagel example exists a function expression FeNCind finite number finite ordinal follows formal formula fraction triplet functional set hence Ibid idea induction inference infinite class lattice lemma Mathematical logic means method notation occur one-to-one correspondence operations pair class paper paradox Paul Bernays philosophy positive real numbers postulates predicate primitive Prof proof propositional calculus propositions proved Quine real numbers recursive reference relation represented reviewer Rosser rules satisfies semantical sentence set theory smor statement subclass symbolic logic tion true University W. V. Quine well-ordering York Zermelo